Question

Bottled Water. A project exploring the bottled-water phenomenon and preference of water types was conducted by researchers M. Lunsford and A. Fink in the article "Water Taste Test Data" (Journal of Statistics Education, Vol. 18, No. 1). One hundred nine subjects participated in double-blind taste tests of three different bottled water brands (Fiji, Aquafina, and Sam's Choice) and tap water. Twelve people preferred the tap water, 27 Aquafino 44 Fiji, and 26 Sam's Choice. At the 5% significance level, do the data provide sufficient evidence to conclude that the four different water types are not equally likely in preference?

Short answer

Ans: The null hypothesis is rejected at $5\%$level.

Thus, the data provided is sufficient evidence to conclude that the four different types of water are not equal in choosing the level of importance.

Step-by-step solution

Step 1. Given information.

given,

A project exploring the bottled-water phenomenon and preference of water types was conducted by researchers M. Lunsford and A. Fink in the article "Water Taste Test Data" (Journal of Statistics Education, Vol. 18, No. 1).

Step 2. Check that the data provide sufficient evidence to conclude that the four different types of water are not equally good at 5% value.

Hypotheses are provided below:

Null hypothesis:

$H_0$:- The data do not provide sufficient evidence to conclude that the four different types of water are not equal in selection.

Another hypothesis:

$H_1:-$ The data provides sufficient evidence to conclude that the four different types of water are not equal in selection.

Step 3. Use MINITAB to get test statistics and P-value.

MINITAB process:

Step 1: Select Status> Tables> Chi-Square-Goodness-of-Fit Test (Single Variables).

Step 2: In the visual calculation, enter the "O" column

Step 3: In the category names, enter the "BRAND" column.

Step 4: Under Test, select the "P" column with seamless values.

Step 5: Click OK.

Step 4. MINITAB Output:

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: O

Step 5. Conclusion: 

Here, the p-value is than the level of significance.

That is, $p-value(=0.000)<\alpha (=0.05)$

Thus, the null hypothesis is rejected at $5\%$level.

Thus, the data provided is sufficient evidence to conclude that the four different types of water are not equal in choosing the level of importance.